MHT CET · Maths · Differential Equations
The population \(p\) of the city at time \(t\) is given by \(\frac{d p}{d t}=\frac{p}{2}-100\).
If initial population is 100 then \(\mathrm{p}=\)
- A \(200+100 e^{\frac{t}{2}}\)
- B \(200-100 \mathrm{e}^{\frac{\mathrm{t}}{2}}\)
- C \(300-100 \mathrm{e}^{\frac{\mathrm{t}}{2}}\)
- D \(300+100 \mathrm{e}^{\frac{t}{2}}\)
Answer & Solution
Correct Answer
(B) \(200-100 \mathrm{e}^{\frac{\mathrm{t}}{2}}\)
Step-by-step Solution
Detailed explanation
\(\frac{d p}{p-200} = \frac{1}{2} dt\) \(\int \frac{d p}{p-200} = \int \frac{1}{2} dt\)
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